Disclaimer: Before we can start, MBTI was “invented” long after Freud died. Therefore, in order to begin to assess his personality, you all need to mark down:

1. the fact that we only know him either through his work
2. the fact that we only know him by the telltales of others.
3. that his writing skills (same as many of us) do not represent the exact personality.
   1. e.g. you see my answer here and you might think: SHE is x,y,z; when in fact I can be a,b,c and you will never know.

There could be other things, but I cannot think about them right now (such as religion, environment, family was poor therefore he wanted to earn some money to support them and he might have done some things etc.)

Premises: So, first of all, we know this:

Based on these he is I(introvert):

1. he did not actually have friends, or at least he did not get too attached
2. he did not enjoy soirees that were very popular back then
3. he did not actually show any interest in “human” aspects, such as socializing even if he had a “clinic” where people came to treat themselves..
4. he enjoyed working in silent mode, parents had to move some furniture around the house to offer him SILENCE to study

Based on these he is N(intuitive):

1. he was a visionary, very imaginative
2. he cataloged things
3. he “created” ideas based on what he observed
4. he even imagined a new branch in Psychology (psychoanalysis)
5. he hated public speaking
6. he loved research
7. he had many attempts to put down his thoughts (MANY) into a single written piece

Based on these he is F(feeling):

1. his scope in life was to help others
2. he wanted to reach the essence of any issue
3. he was really stubborn, and he did not accept the fact that someone else was right and he was wrong
4. he believed that his moral compass was working fine (until it didn’t anymore…)

Based on these he is P(perceive):

1. he did not enjoy planning too much, he would rather be spontaneous
2. he enjoyed a little adventure

Conclusion: He might have been an INFP but … Please feel free to add or to question everything. I myself am not even sure that the above is correct.